Pseudo-Anosov stretch factors and homology of mapping tori

Ian Agol; Christopher J. Leininger; Dan Margalit

doi:10.1112/jlms/jdw008

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arXiv · 1409.6983

Pseudo-Anosov stretch factors and homology of mapping tori

Ian Agol·Christopher J. Leininger·Dan Margalit

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Abstract

We consider the pseudo-Anosov elements of the mapping class group of a surface of genus g that fix a rank k subgroup of the first homology of the surface. We show that the smallest entropy among these is comparable to (k+1)/g. This interpolates between results of Penner and of Farb and the second and third authors, who treated the cases of k=0 and k=2g, respectively, and answers a question of Ellenberg. We also show that the number of conjugacy classes of pseudo-Anosov mapping classes as above grows (as a function of g) like a polynomial of degree k.

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BibTeX RIS

Ian Agol, Christopher J. Leininger, Dan Margalit. 2015-03-04. Pseudo-Anosov stretch factors and homology of mapping tori. https://doi.org/10.1112/jlms%2Fjdw008

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